•Sensitivity analysis (SA) approach is used to quantify the effects of correlated input parameters on model outputs.•Penalized spline regression model is used to approximate complex data. We provide a sensitivity analysis toolbox consisting of a set of Matlab functions that offer utilities for quantifying the influence of uncertain input parameters on uncertain model outputs. It allows the determination of the key input parameters of an output of interest. The results are based on a probability density function (PDF) provided for the input parameters. The toolbox for uncertainty and sensitivity analysis methods consists of three ingredients: (1) sampling method, (2) surrogate models, (3) sensitivity analysis (SA) method. Numerical studies based on analytical functions associated with noise and industrial data are performed to prove the usefulness and effectiveness of this study.